Key insights into the behaviour of the Dirichlet Process were given by
[1]} and [2]}. [2]}
derives a conditional prior for the class labels, \({\bf c}\) , by viewing the Dirichlet
Process mixture model as the limit of finite mixture models as \(K \rightarrow \infty \) .
By integrating out the mixing parameters \({}\)  he gives the following
conditional priors for the elements of \({\bf c}\)
\(P(c_i = k | {\bf c}_{-i} ) = \frac{n_{-i, k}}{N - 1 + \alpha } \\P(c_i \ne c_j \text{ for all } i \ne j | c_{-i}) =\frac{\alpha }{N - 1 + \alpha }\) 
